Mr Zakharchenko, a native of east Ukraine, has replaced Russian national Aleksander Borodai as the leader of the self-proclaimed, pro-Russian Donetsk People's Republic amid initial hopes he would bring a de-escalation in the conflict.
But yesterday Mr Zakharchenko told journalists a counter offensive was being prepared.
The warning came as the Ukrainan military said Russia has massed 45,000 troops on its border with Ukraine, backed by an array of heavy equipment, including tanks, missile systems, warplanes and attack helicopters.
A Ukrainian spokesman said: "About 45,000 troops of the armed forces and internal forces of the Russian Federation are concentrated in border areas."
He said they were supported by 160 tanks, 1,360 armoured vehicles, 390 artillery systems, up to 150 Grad missile launchers, 192 fighter aircraft and 137 attack helicopters.
President Vladimir Putin said Moscow was sending an aid convoy into the country.
Nato Secretary-General Anders Fogh Rasmussen had warned there was a "high probability" Russia could launch an invasion of Ukraine, possibly under the guise of a humanitarian operation aimed at helping pro-Russian communities.
European Commission President Jose Manuel Barroso warned Mr Putin against military intervention in Ukraine in telephone talks yesterday.